property

magnetic moment

A measure of an object's tendency to align with a magnetic field, arising from its spin and orbital motion.
11 related articles · 1 formulas

Description

The magnetic moment is a vector quantity that measures the strength and orientation of a particle's or object's tendency to align with an external magnetic field. It arises from two sources: the intrinsic spin of particles (like electrons) and their orbital motion around a nucleus or within a current loop. The magnetic moment is fundamental to understanding magnetism at all scales, from individual atoms to entire stars.

History

The concept of magnetic moment was developed in the 19th century, but its quantum treatment began with the work of Wolfgang Pauli and others in the 1920s. The precise measurement of the electron's magnetic moment (the anomalous magnetic moment) became a cornerstone of quantum electrodynamics and a test of the Standard Model.

How it works

For a charged particle, its spin creates a tiny circulating current, which generates a magnetic field — this is the spin magnetic moment. Similarly, an electron orbiting a nucleus produces a magnetic moment like a tiny current loop. In an external magnetic field, these moments experience a torque that tries to align them with the field. The magnitude of the magnetic moment determines how strongly the object interacts with the field, and its quantum nature means it can only take discrete orientations.

In practice

Magnetic moments are exploited in MRI imaging (where proton moments align in a magnetic field), in data storage (magnetic domains in hard drives), and in quantum sensing — for example, using nitrogen-vacancy centers in diamond to detect tiny magnetic fields from single spins.

Fun fact

The electron's magnetic moment is one of the most precisely measured quantities in physics, agreeing with theoretical predictions to better than one part in a trillion — one of the most accurate tests of any theory in science.

Concept graph →

Formulas

$$H_{\text{HFI}} = \boldsymbol{\mu}_I \cdot \mathbf{A} \cdot \mathbf{S}$$
Interaction between nuclear and electron magnetic moments.
What is in the formula
H_{\text{HFI}}variablemagnetic hyperfine interaction Hamiltonian — hamiltonian joule
\boldsymbol{\mu}_Ivariablenuclear magnetic moment — magnetic moment ampere square metre
\mathbf{A}variablehyperfine coupling tensor — tensor joule per ampere square metre
\mathbf{S}variableelectron spin operator — spin operator
\cdotoperatorscalar product of vectors — dot product

Related articles · 11

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Mesoscale2026-09-042 minarXiv:2609.05668
A Gyroscope That Hears Magnetic Echoes
An interpreter gets distracted by every rustle in the hall, and a one-hour meeting stretches into two. The same happens with a capacitive gyroscope: to hear the nanometer-scale displacement of its proof mass, it needs perfectly tuned gaps between the plates. The smaller the sensor, the harder it is to maintain that precision.
A Compass for Black Holes
In 2015, the LIGO detectors caught the first ripple of spacetime from a black hole merger. Since then, hundreds of such events have piled up, each carrying the imprint of its ancestry: whether the holes were born together from a single pair of stars or met by chance in a dense cluster. The difference shows in the direction of their spin axes.
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How Quanta Carry Away Spin from Stellar Pairs
Two stars circle each other, gradually drawing closer. Their dance loses energy, and that energy escapes into space — in the form of gravitational waves, and sometimes other fields.
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Why Left- and Right-Handed Molecules Conduct Electricity Differently
A spiral staircase sets the rhythm of footsteps: if a stream of people runs up it, their motion inevitably twists. Something similar happens in helical molecules — for example, in DNA or certain proteins. When an electric current is passed through such a molecule, electrons don't just fly straight.
Materials2026-05-232 minarXiv:2605.24320express
Magnetic Dualism in a Crystal
A translator works in two worlds at once: to an outside observer, they are silent and unobtrusive, but inside their mind, a flurry of activity unfolds along clear lines of meaning. Altermagnets, a recently discovered class of magnetic materials, are much the same.
HEP Theory2026-05-191 minarXiv:2605.19817express
Gravitons: A Double Twist in a Curved World
Gravity is the curvature of spacetime, not just an attraction, as Einstein showed. On such a curved "dance floor", even the hypothetical carriers of gravity — gravitons — move oddly.
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Light bends around massive bodies: this has been known since Einstein's time. But what if gravity itself is not a smooth fabric of space but a stream of tiny carrier particles? Then a beam passing near a particle should not just bend but enter into a special quantum relationship with it. This relationship is called entanglement.
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Electronic Vortices Sang on Nanostrings
In the cold heart of a pure crystal, electrons flow like a viscous fluid — an idea predicted by Lev Landau. But the vortices of this fluid remained invisible, like a painting inferred from the noise of a crowd. Now scientists have created a nanostring: a semiconductor tuning fork with a circular cavity.
Quantum Physics2026-01-201 minarXiv:2601.14381express
Magnetic field turns the void into a motor
Two metal plates in a perfect vacuum attract each other. Even Richard Feynman compared emptiness to a boiling foam: particle pairs are born and immediately vanish, creating the Casimir effect. If the plates are asymmetric, they also start to twist — that's a vacuum motor. But rotation doesn't require oddly shaped parts.
Quantum Physics2025-11-101 minarXiv:2511.07220express
How Time Can Run Backwards
We’re used to time flowing only forward. But quantum laws let it become like a coin showing heads and tails at once. Take a particle with its own spin — its intrinsic rotation. In a magnetic field, it spins like a top. Send this particle through a device where two opposing magnetic flows fight each other — and it will start moving into the future and the past at the same time.